The Soot Free Company operates in a purely competitive chimney cleaning industry

Question

The Soot Free Company operates in a purely competitive chimney cleaning industry in Ottawa. Its short run costs are: • Total cost = 40+10Q+0.10Q2 (Q = the number of chimneys cleaned per day); • Marginal cost = 10+0.2Q .

1. If the Soot Free Company charges $20 to clean a chimney, how many chimneys (Q) must it clean every day to maximize its profit?

a) 10; b) 20; c) 40; d) 50.  

2. What is the dollar average cost of cleaning a chimney cleaned based on your answer to question 1?

a) 5.50; b) 12.40; c) 15.80 d) 17.80.  

3. What is the daily dollar fixed cost of cleaning chimneys?

a) 20; b) 25; c) 30; d) 40.

4. What is the daily total revenue based on your answer to question 1?

a) $500; b) $670; c) $1000; d) $1200.

5. What are Soot Free Company’s profit based on your answer to question 1?

a) $90; b) $210; c) $790; d) 1000.

Explanation / Answer

Answer

1) The correct option is (d) 50

As it operates in pure competitive industry

Hence Profit Maximizes at that quantity where

P = MC

=> 20 =  10+0.2Q

=> Q = 50

2) The correct answer is (c) 15.8

AC = TC/Q

At Q = 50, TC = 40 + 10Q + 0.10Q2 = 40 + 10*50 + 2500*0.1

=> TC = 790

Hence AC = TC/Q = 790/50 = 15.8

3) The correct answer is (d) 40

TC = 40+10Q+0.10Q2

Fixed cost is that cost which does not depend on Q. That is Fixed cost is that cost which incur even when Quantity = 0 and Fixed cost is constant.

At Q = 0, TC = 40

this implies Fixed cost is 40

4) The correct option is (c) $1000

Total Revenue(TR) = Price *Quantity = 20*50 = 1000

5) The correct answer is (b) $210

Profit = TR - TC

= 1000 - 790(calculated in (2))

= 210

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